Smith55 has used the notation of naming each column in the puzzle as a letter from a to i. For example, Column 1 is represented by the letter "a" and Column 5 is represented by the letter "e". After that, each Row is simply represented by the number of the Row.

Therefore, in his first step, he refers to "5i5". This means he placed the number 5 in Column9, Row 5. In his second step, he palced the number 8 in Column 5, Row 4. And so on.

Personally, I think it's a lot easier to simply refer to them by their designated places in the Rows and Columns. For example, I would refer to the cell "i5" as cell number r5c9.

One might almost argue that this move should have been preceded by 5e3, which is actually recorded as the 7th move in the solution posted above. No matter -- here's the explanation.

Notice the values {7, 9} lying in columns 4 & 6. Because of the way these are positioned, the values {7, 9} must fit in r7c5 and r9c5 in the bottom center 3x3 box ... there's no other way to fit either of them in that box. So the "5" in the bottom center 3x3 box has to fit in r8c6 -- there's nowhere else left for it.

This formation (the {7, 9} in r7c5 and r9c5) is known as a "hidden pair." dcb

Solved the puzzle, but, I still do not see why you can assign 1 to i9 at step 10. Could somebody explain this?

-- There has to be a "1" in row 9 somewhere.

-- It can't go in r9c1 or r9c3 because of the "1" at r8c3.

-- It can't go in r9c5, either, because of the "hidden pair" {7, 9} that occupies r7c5 & r9c5. Note the {7, 9} pair in column 4, and also in column 6 -- it's clear that the two digits "7" and "9" _must_ occupy the two cells r7c5 & r9c5, because there's no other way to fit these two digits into the bottom center 3x3 box.

Are we to have a poll on the time taken for evey puzzle?
If so, perhaps this should be a feature of the site rather than
being left to the initiative of a forum user.

However, I fail to understand what one may glean from the
results of the poll. It all comes down to the "sampling frame".
With the methodology adopted there is a lot of self-selection.
In particular those who do not finish will not enter as there is
no "radio button" for [unfinished] - and even if there were, one
would have to consider what should happen if someone who has
it unfinished subsequently completes the puzzle.

+++
For the record, I found this one fairly difficult - and had to move
from Mandatory Pairs to significant analysis of Candidate Profiles
in order to reach the solution.

I find Candidate Profiles difficult in that they require meticulous
attention to detail and one error can negate everything. As such, I
needed two goes at this one. The first lasted about an hour, got
bogged down in profiles and resulted in an error due to negligence
on my part. Start again! The second time (with no reference to my
work sheet from the first time), the puzzle came out in under an
hour. There are some puzzles where the Mandatory Pairs approach
turns out to counter-productive and this may well have been one of
them - although I did use it before before and after the work done
on creating and scanning the Candidate Profiles.

I think so. It's a consequence of the hidden pair {7, 9} in r7c5 & r9c5. In fact, I can't even notice the triplet {1, 2, 3} that remains in column 5 until I've entered the "5" at r3c5.

The only reason I said "5. 5e3" might be a more natural move than "5. 5f8" is psychological -- it's a matter of where one focuses one's attention. Logically, both moves are pretty simple once one notices the hidden pair {7, 9} at the bottom of column 5.

I saw the {7, 9} pair in two places -- in r1c4 & r4c4, and also in r1c6 & r4c6. Since r8c5 was already occupied, I recognized that the pair {7, 9} was going to fill the cells r7c5 & r9c5. But since my attention was already focused on the top center 3x3 box and I was thinking about column 5, I naturally noticed the "5" at r3c5 before I thought about the one at r8c6, and that's all. dcb